Nonlinear Quantum Fluctuations Near Bifurcations

Abstract

Intracavity nonlinear optical systems exhibit a variety of bifurcations. Quantum fluctuations in the vicinity of these classical instability points have been much studied since they can lead to novel quantum states such as squeezed light’. The calculation of dynamical correlations is usually made by linearizing the quantized fields around a classical steady state. This breaks down when the quantum fluctuations are sufficiently large: for example, in the strongly coupled regime of cavity QED, or near to a classical bifurcation point (or both). We developed a microscopic approach to understand nonlinear quantum fluctuations in terms of resonant multiphoton scattering from intermediate states which produce a “many-photon” polarization of the cavity modes^2,3. This manifests itself in a macroscopic dependence of field correlations on characteristic photon number. Analogies with the quantum fluctuations of a partially condensed Bose gas also arise with this approach.